Subtraction with Renaming

May 17, 2015

Standards for Math Practice 4

We have moved on to subtraction with renaming (2.NBT.7). You might call this regrouping… but really- if we think literally about what’s happening- we’re also giving the values new names! 50+10 is a different name for 60. So, renaming, regrouping… you know what we’re doing!

What’s Working

I’ve been doing a lot of this work with students in small groups. It’s amazing to see students talking and thinking about making trades, or renaming numbers. In a small group full of dialogue, students physically traded one of the ten rods that makes up 60 for 10 unit cubes, so they can more easily subtract 13. We talked about the value of 60 at the start, during and after the trade. Students giggled about how I could still buy exactly 60 $1 ice cream cones- no more, no less; at every phase of the trade. They knew that whether 60 was composed of 6 ten rods (60+0) or 5 ten rods and 10 unit cubes (50+10), its value remained constant.

We worked through a few more bare number problems that also required renaming to get more ones and I really emphasized how accurately our recording matched their physical manipulation of the base ten blocks as well as their thinking. Students recorded on white boards, just as I had… and I expected we were good to go! Not so fast. About 1/3 of my students were not able to demonstrate their learning with much independence… even with 60-13. Even if I talked about ice cream cones. These students seemed to rely heavily on the scaffolding that came from our discussion throughout the trading process.

Now What?

So, I decided they needed a trading center– a place where they could be successful and independent with the skills that this high level work demanded. Here are some of the recording sheets that are guiding their work. I needed them to build confidence and more deeply conceptualize the equality of the value of the numbers they were composing, both before and after renaming. They needed to deepen their understanding that values can be represented in multiple ways. After observing students’ success with this work in centers, I realized this center had potential value for all of my students. It provides an opportunity for students to focus on and practice their recording, outside of the context of the subtraction problem itself.

Additionally, it is forcing some of my higher level students to build, revisiting a more concrete experience with numbers. This helps me prepare them to rename to get more tens, hundreds etc. They are finding the challenge numbers particularly fun to work with, and I appreciate the opportunity for students to grapple with these situations in isolation, as opposed to in the context of a subtraction problem. Having this more isolated experience, makes them more confident, and less distracted by the challenge in the midst of a problem. I hope these ideas work as well for your kiddos as they did for mine!!

💔Not all of the homes our students live in, are meant for a 24/7 quarantine. Not all of the adults who live with children can handle the added pressure. For many of our students, school has been an escape, a respite, a safe haven- from their home lives. And that escape was taken 3 months ago without warning.

🛎 I’ve come to appreciate in recent months, the vital role public school departments play in our communities. The scale of the work has been much grander than the academics and due dates. There are mobile food stations and wellness checks, phone calls and internet setups. There are intuitive teachers recognizing that “something’s just not right” and administrators encouraging them to trust their instincts.

🌼Kids are resilient. Often, they are so strong and brave, you’d never guess where they’ve been.

🌈The WHOLE picture is a big one right now. Before you judge a decision, know that there’s a whole lot you do not know. And know, that everyone involved has the best of intentions. I am in awe of the amazingly thoughtful and important work being done by my educator colleagues in schools all over right now. ...